Question

Unit of acceleration due to gravity is:
(A). $m{{s}^{-1}}$
(B). $m{{s}^{-2}}$
(C). $m{{s}^{-3}}$
(D).$m{{s}^{-4}}$

Answer 1

Hint: Convert the mathematical formula of retardation into basic measurement units in the SI system. From the basic definition of acceleration, one can find out the basic quantities that contribute in acceleration.
Formulae used: The basic formulae derived from the definition of acceleration and velocity are used. i.e. $\text{acceleration}=\dfrac{\text{change in velocity}}{\text{change in time}}$ and $\text{velocity}=\dfrac{\text{change in displacement}}{\text{change in time}}$

Complete step by step answer:
The International System of Units (SI) was introduced to standardize the measurement units across every system and place. For example, if a quantity is measured somewhere then, all around the world the interpretation should be the same. This system promises uniformity in measurements. There are seven base units of measurements.
Second (s): unit of time
Meter (m): unit of time length
Kilogram (kg): unit of time mass
Ampere (A): unit of time electric current
Kelvin (K): unit of thermodynamic temperature
Mole (mol): unit of amount of substance
Candela (s): unit of luminous intensity
Acceleration due to gravity is the acceleration an object experiences during a free fall on Earth’s surface. But, the SI unit for all the types of acceleration must remain the same. Therefore, from the basic definition, for an object, acceleration is defined as the rate of change of the velocity with respect to time. Whereas, the velocity is defined as the rate of change in its displacement with respect to time.
The equation for acceleration is:
$\text{acceleration}=\dfrac{\text{change in velocity}}{\text{change in time}}$
Similarly, the equation for velocity looks like,
$\text{velocity}=\dfrac{\text{change in displacement}}{\text{change in time}}$
We know, displacement is a measurement of length, with SI unit $m$, and time has SI unit $s$. Therefore, Substituting the SI units in the equation of velocity, we get the SI unit of velocity as $\dfrac{m}{s}$ .
Now, we substitute this SI unit of velocity into the equation of acceleration. To obtain
$\dfrac{\dfrac{m}{s}}{s}=\dfrac{m}{{{s}^{2}}}$
Which means the SI unit of retardation is option B. $m{{s}^{-2}}$ .

Note: Any kind of acceleration, even acceleration due to gravity is essentially acceleration and the SI units will not change. For example, force due to a physical impact, force to gravitation and all types of forces will all have the same SI unit, that is newton.